The present invention relates to a process for measuring the movement of city areas and landsliding zones.
As is already known, a synthetic aperture radar or SAR produces a bi-dimensional image. One dimension of the image is called range and it is a measurement of the line-of-sight distance from the radar to the object illuminated. The other dimension is called azimuth and is perpendicular to the range.
The measuring operation and the range accuracy are obtained by means of a synthetic aperture radar determining as precise as possible the time that has passed from the transmission of one pulse by the radar to receiving the echo of the illuminated object. The range accuracy is determined by the length of the pulse transmitted. Shorter time pulses ensure a finer resolution.
To obtain a fine resolution of the azimuth it is necessary to use a large physical antenna so that the electromagnetic wave transmitted and received is as similar as possible to a pulse (in the ideal case the pulse has the shape of a Dirac delta).
Similar to optical systems (such as telescopes), that need large apertures to obtain fine resolutions of the image, also a SAR-type radar, of normal precision, that works at a much lower frequency than those of the optical systems, needs an enormous antenna with enormous apertures (hundreds of meters), that cannot be installed on any platform. Nevertheless a SAR-type radar installed on an aeroplane can collect information during the flight and then elaborate it as if it were an antenna. The distance that the aeroplane covers, simulating the length of the antenna, is called synthetic aperture.
The SAR-type radar consists of a coherent radar, that is a radar which measures both the module and the phase of the electromagnetic wave reflected, operating at a frequency which is usually between 400 Mhz and 10 Ghz, and is, as previously said, installed on aeroplanes, and also on orbiting satellites at a height between 250 and 800 Km.
The antenna of the radar is directed towards the earth orthogonally to the direction of the movement of the platform (aeroplane or satellite) with an angle, called xe2x80x9cOffnadirxe2x80x9d, between 20 and 80 degrees in relation to the direction of Nadir, that is, perpendicularly to the earth.
With said system, resolution cells or grids of the earth surface can be generated with a spatial resolution of a few meters. Said cells present a minimum grid of resolution, that is, they have a spacing within which it is possible to distinguish two objects to illuminate.
The most important characteristic of SAR is that it is a coherent image system. It is therefore possible to measure the range difference in two or more SAR images (SAR interferometer) of the same surface with an accuracy of a fraction of the SAR wavelength.
Using focusing techniques that preserve the phase, images are obtained in which every element of the image (pixel) is associated with a complex number resulting from the combination of the backscattering of all the objects belonging to the same ground resolution cell and the phase rotation due to the path.
The phase of every pixel is given by the sum of two terms: the first is the phase of the scatterer xcfx86s and the second is given by xcfx86r=4xcfx80r/xcex, where r is the radarxe2x80x94resolution cell distance and xcex is the radar wavelength (with xcex=c/(2xcfx80f), where f is the operating frequency of the radar and c is the speed of the light). The second phase term contains millions of cycles because the wavelengths are a few centimeters and the radar sensorxe2x80x94resolution cell distance is a few hundred kms, while the displacement connected to the scatterers is fundamentally random and therefore the phase of a single SAR image is practically unusable. However, if we consider the phase difference between two SAR images taken from slightly different viewing angles, the phase term due to the scatterers is cancelled (at least in first approximation if the angle difference is small) and the residual phase term results xcfx86=4xcfx80xcex94r/xcex where xcex94r is the difference of the paths between the sensors and the same ground resolution cell. The phase term still contains a very high number of cycles, that is known apart from the high integer multiple of 2xcfx80, but passing from one resolution cell to an adjacent one, the variation of the phase is usually small enough not to present ambiguity of 2xcfx80. The phase thus deduced is called the interferometric phase and the variation information xcex94r (which is measured in fractions of wavelength xcex) between pixel of the SAR image is connected thereto. Knowing the position of the two sensors, the measure of xcex94r can be used to find the relative elevation between the pixel of the image and therefore generate a digital elevation model (xe2x80x9cDigital Elevation Modelxe2x80x9d or DEM), that is, an electronic reading is taken of the topography of the Earth""s surface. On the other hand, if the topography is known, that is a DEM of the area of interest is available (there are special data banks from which one can take these digital models), its contribution to the interferometric phase can be eliminated and possible small surface displacements can be detected. In the case of the satellites ERS-1 and ERS-2 (twin satellites sent into orbit by the European Space Agency, the first, ERS-1, in 1991, the second, ERS-2, in 1995, operating at a frequency of 5.3 GHz, characterised by a 35-day revolution period and by a 20-meter grid resolution), for example, from one passage to the next of the platform (ERS-1 and ERS-2 follow each other at a distance of one day), or of one of the two satellites, several scatterers do not change their behaviour, that is, they keep a high coherence and therefore the cancellation of their phases is practically perfect. This means that the phase measures obtained by means of this technique can measure movements that are even a few millimeters of the Earth""s topography.
Nevertheless, the present techniques of differential interferometry have some limits. In fact after a few days, in extended zones, the scatterers lose coherence, that is the scatterers do not remain similar to themselves after a period of time and therefore coherent zones with dimensions exceeding a few resolution cells cannot be identified. In addition, the wavelength of the incident signal and the displacement of it are function of atmospheric conditions. These cause phase rotations that cannot be distinguished from the movements of the ground that are required to be measured.
Another problem is the physical structure of the single scatterer that influences the phase variation in function of the observation direction and therefore of the baseline, that is of the distance between the two satellites projected orthoganally to the view line. If the stable scatterer is a surface that backscatterers and that occupies the entire resolution cell in the range, the phase of the radar echo loses correlation in correspondence with the so called critical baseline (for example in the case of satellites of the ERS type the critical baseline is about 1200 meters). When instead the scatterer is pointwise or is a comer reflector, the phase remains unvaried for much greater baselines.
In view of the state of the art described, the object of the present invention is to identify a measuring process, which resolves the problems of the present techniques so that the movement of city areas and landsliding zones can be measured in a more reliable manner.
According to the present invention, such object is reached through a process for radar measuring of the movement of city areas and landsliding zones which, having available N greater than 20 images taken with a Synthetic Aperture Radar or SAR over a multi-year period, identifies, for every resolution cell, the scatterers, called permanent scatterers PS, that keep their electromagnetic characteristics unchanged over time, characterized in that said PSs are identified through the following steps:
(a) Nxe2x88x921 differential interferograms are formed in relation to the main image, called master, using a digital elevation model or DEM with vertical accuracy better than 50 meters;
(b) for every pixel of the image of point (a) selected on the statistical properties of the modulus of the reflectivity, a temporal series of the interferometric phases is generated, and then, spatial differences among temporal series that belong to neighbouring pixels are formed;
(c) for every differential temporal series of point (b) the linear phase components are calculated in relation to the baseline and the phase components connected to the displacement model, already known, in relation to the time;
(d) the relative error between the precise elevation of the pixel supplied from DEM of point (a) is associated with the linear phase component of point (c) in relation to the baseline;
(e) the relative movement of the pixel in the direction of the SAR is associated to the polynomial phase variation in relation to the time of point (c);
(f) the phase residuals are formed by subtracting the contributions calculated at points (d) and (e) after a phase unwrapping procedure on the sparse grid of the selected pixels;
(g) the spectral power density of the phase residuals is analysed and (g.1) if the residuals relating to each single image are spatially correlated, attributed to atmospheric artefacts and removed; if (g.2) the further residual dispersion relating to each single image is too large the pixel is discarded.
Said process is characterised in that given a number of PS per surface unit greater than 25 per Km2, after the elaboration of the phase residuals, the atmospheric artefact of every single image is determined by subtracting said artefact from the vertical precision of the DEM.
Thanks to the present invention, a process can be made for identifying the stable scatterers in time, called PS (regardless of the atmospheric conditions and of the type of platform on which the SAR radar is positioned), which can determine the movement of city areas and landsliding zones.
As well, a process can be provided which makes it possible, from the phase dispersion of the PS, to estimate the dimension and construct a network of natural reflectors suitable for identifying the orbital position of any satellite or aeroplane that illuminates the natural network of said PS, or to measure the movements of the PS or of the atmospheric artefact.